They host Castleford Tigers tomorrow just two points clear of London Broncos at the bottom.
The West Yorkshire club are out of form at a critical time and were embarrassed 44-0 by struggling Leeds Rhinos on their last home appearance.
There were more positive signs in the 32-12 loss at Salford last week when Woolford’s side actually led late on.
“We’re all under pressure but we have to deal with it,” said Woolford.
“We have to find good performances under pressure. That’s what it’s all about at the moment.
“We’re still in a position where we control our own destiny. We need to make sure the effort we had last week is there for the next four games.”
Key forwards Matty English and Joe Wardle miss out with injury so Sam Hewitt and Adam Walne come into the squad.
Castleford are chasing a top-five spot but Giants have beaten them 20-18 at John Smith’s Stadium in April and only lost out in Golden Point extra-time at Wheldon Road.
“We had that game in the bag the second time at The Jungle,” recalled Woolford.
“But we threw that one away having led going into the final few minutes. It sounds funny but we do have a bit of confidence going in to this; we are confident we can play well and beat Cas. But the pressure needs to bring the best out of us.”